Cremona's table of elliptic curves

8112 = 2⁴ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3+ 13-	Signs for the Atkin-Lehner involutions
Class	8112z	Isogeny class
Conductor	8112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	14976	Modular degree for the optimal curve
Δ	1527047909712 = 24 · 32 · 139	Discriminant
Eigenvalues	2- 3+ -2 -4  6 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2929,14728]	[a1,a2,a3,a4,a6]
Generators	[52:18:1]	Generators of the group modulo torsion
j	16384/9	j-invariant
L	2.7387242019083	L(r)(E,1)/r!
Ω	0.73698624308545	Real period
R	3.7161130585591	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2028f1 32448dk1 24336cd1 8112x1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112z1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	-2	-4	6	-	2	0	-8	2	-8	8	2	-8	6	6	2	2	4	6	-4	0	14	6	12

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Quadratic twists for elliptic curve 8112z1

-4	8	-3	13
2028f1	32448dk1	24336cd1	8112x1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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